Johnny847 has explained the pitfalls and rationale quite well. From my own limited experience doing this and from reading on Flyertalk, you should be fine with putting your frequent flyer number on the ticket anyway, as long as you're not doing this all the time.
Be aware that you're violating the terms and conditions of your ticket when you do this. That probably doesn't matter, but if you do the same route regularly, after a couple of missed final segments the airline's computers will notice you, and the airline may cancel your remaining tickets. Yes, you could probably sue them and maybe win, but you probably wouldn't bother.
Optimal strategy, probably: do it occasionally, not regularly on the same route or with the same airline, and only when the payoff is big. For example, because Air Canada has to compete on price/inconvenience on tix from the US to Europe, NYC-Europe is often slightly cheaper than NYC-Europe on American carriers and much cheaper than Toronto-Europe on Air Canada. So Torontonians might want to get to NYC somehow, fly to Europe via Toronto, then fly back to "the US" and just get off the plane in Toronto. Or fly Toronto-Europe-"NYC" and save less money, but also avoid the hassle of getting to NYC in the first place.
"Somebody I know" did this last year to get to Istanbul, and saved about $400.